The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.
Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 10, 2014; final manuscript received November 20, 2015; published online February 17, 2016. Assoc. Editor: Fu-Cheng Wang.
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Dhanda, A., Vaughan, J., and Singhose, W. (February 17, 2016). "Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions." ASME. J. Dyn. Sys., Meas., Control. April 2016; 138(4): 041006. https://doi.org/10.1115/1.4032064
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